One should not use a metal skewer to roast the korban Pesach. This is due to the fact that the Torah requires us to roast korban Pesach on an open fire (צלי אש). A metal skewer can be heated up to a very high temperature and roast the meat that it touches (which would then not be roasted by an open fire). [1]
The best skewer to use for roasting the korban Pesach is a branch of a pomegranate tree. Branches from other trees may release sap when heated, which would be a problem, because the Torah tell us that korban Pesach may not be cooked. [2]
[1] רמב“ם פרק ח מהל ‘קרבנות הלכה ט [2] שם הלכה י